Do Ys and Trails series take place in the same World/Universe, but at different eras?

Like maybe Ys takes place thousands of years before Trails series, back when the fictional Earth still had 2 moons. But maybe the second moon got destroyed somewhere down the line during a cataclysm/war.

And does Tokyo Xanadu exist in the Trails world? I think I've heard a Trails character makes a cameo in Xanadu, but I don't know for certain.